Respuesta :
Answer:
The angular frequency, maximum speed and maximum acceleration are 2826 rad/s, 1.95 m/s and 5510.53 m/s².
Explanation:
Given that,
Frequency = 450 Hz
Amplitude = 0.690 mm
(I). We need to calculate the angular frequency
Using formula of angular frequency
[tex]\omega=2\pi f[/tex]
Put the value into the formula
[tex]\omega=2\times3.14\times450[/tex]
[tex]\omega=2826\ rad/s[/tex]
(II). We need to calculate the maximum speed
Using formula of the maximum speed
[tex]v_{max}=\omega A[/tex]
Where, A = amplitude
Put the value into the formula
[tex]v_{max}=2826\times0.690\times10^{-3}[/tex]
[tex]v_{max}=1.95\ m/s[/tex]
(III). We need to calculate the magnitude of the maximum acceleration
Using formula of the maximum acceleration
[tex]\alpha_{max}=\omega^2 A[/tex]
Put the value into the formula
[tex]\alpha_{max}=(2826)^2\times0.690\times10^{-3}[/tex]
[tex]\alpha_{max}=5510.53\ m/s^2[/tex]
Hence, The angular frequency, maximum speed and maximum acceleration are 2826 rad/s, 1.95 m/s and 5510.53 m/s².
